Solve 2 to the x = 9 , what is x=? Can you solve this type of Algebra Equation?

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14 окт 2024

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Комментарии : 68

@dazartingstall6680 19 часов назад

Interesting use of the phrase "round it off" there. log9 ÷ log2 = 3.169925... Rounding that off to three decimal places, we get 3.17. (The third place would be a nought, which we can omit.) 3.169 is a truncation, not a rounding.

@jenohathazi920 19 часов назад

it's correct

@dazartingstall6680 19 часов назад

@@jenohathazi920 I didn't say it's not correct. But it's a correct truncation, not, as John called it, a rounding off.

@tomtke7351 19 часов назад

2^x = 9 off top x=1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 guess x = 3.2 for 2^x=9 this is an excellent problem for logs. log a = b or 10^b = a further loga^x = xloga [basic log rule] log2 = x where 10^x = 2 log2 = 0.3010 log9 = 0.9542 [found on calculator but back in my day we looked up these numbers in the back of our text book in log tables because we had no calculators. We even had logs of trig functions. The little black book for the engineer exam has (or ¿had?) these tables.] 10^0.3010=1.9999, =2 10^0.9542=8.9991, =9 here 2^x = 9 same on either side=> log { 2^x = 9 } log(2^x) = log(9) xlog2= log9 x= log9/log2 = 0.9542/0.3010 = 3.1699 our previous guess = 3.2 V E R I F Y (calculator) 2^3.1699 =? 9 8.9998 =❤ 9✔️

@dazartingstall6680 18 часов назад

Further verification, again with a calculator: 2^(log9 ÷ log2) = 9 I also remember log tables. We had them in a thin book that also contained sine, cosine and tangent tables.

@petervladyevich8535 18 часов назад

2^x=9 exponential writing e^(x ln(2))=e^ln(9) x ln(2)=ln(9) x=ln(9)/ln(2) Thank you it's a pleasure to ear your explanations

@imagseer 19 часов назад

I remember this from when we were taught about logs and slide rules! - Early 1960s. Thank you for stirring the memory.

@tomtke7351 19 часов назад

add in: the slide rule is logarithmic laid out to essentislly ADD together two numbers' logs when multiplying them.

@todd5291 5 часов назад

My goodness, so many tangents you went on, one can get lost in the point! I could not bear to finish it...

@memirandawong 15 часов назад

These problems are painfully fun to review. I haven't forgotten everything!

@johnmarchington3146 13 часов назад

I looked up my Chambers seven decimal place log tables and found that log 9 (to base 10) was 0.9542 (to four decimal places) and log2 was 0.3010, so 0.9542/0.3010 = approx, 3.17 for x.

@mrpunch72 18 часов назад

May I ask what application you use for the "chalkboard "?

@nancyholcombe8030 17 часов назад

I understood from basic knowledge of exponents that it would be 3-something. Thanks for explaining what a logarithm is!😊

@colturn68 19 часов назад

If you took log to the base of 2, then the LHS would resolve to x. Then x=log base 2 of 9

@jamesharmon4994 6 часов назад

This is exactly my answer.

@TheSimCaptain 5 часов назад

The only problem is you won't find log to the base 2 in your calculator. You're still left with the same problem of finding the arithmetic value.

@jamesharmon4994 5 часов назад

@@TheSimCaptain that's funny, I can do it on mine - it allows choosing your base.

@TheSimCaptain 5 часов назад

@@jamesharmon4994 Not on most calculators. But you still need a calculator, as log base 2 of 9 isn't an arithmetic solution.

@dazartingstall6680 20 часов назад

2ˣ = 9 log2ˣ = log9 x(log2) = log9 x = log9/log2 (I hope)

@mikesheth5370 16 часов назад

Yes simple if you know Logarithme solution. Log on base 10. Look up tables and solved.Log on base 10 for 4.5.

@dazartingstall6680 11 часов назад

@@mikesheth5370 log9/log2 isn't the same as log(9/2).

@jamesharmon4994 6 часов назад

This is also equal to log base 2 of 9.

@mikesheth5370 3 часа назад

@@dazartingstall6680 Have to check like g theorems! Can find log value on base 10 for 9 and 2 and divide.

@dazartingstall6680 Час назад

@@mikesheth5370 I assumed 9/2 was how you'd arrived at 4.5. We find the base 10 log of 9 We find the base 10 log of 2 We divide the former by the latter The number 4.5 does't appear anywhere in this calculation.

@kevingilliam6807 15 часов назад

I just rewrote the original equation as a log equation. log base 2 (9) = x. Which can be rewritten using rules of logs as Log 9/Log 2.

@russelllomando8460 20 часов назад

thanks for the lesson

@clivewilliams3661 7 часов назад

Just goes to show that 55 years old maths teaching still works!!!! (PS I solved it within a minute)

@mikesheth5370 16 часов назад

Simple! If you know log solution . Log of both side. and power can be multiplied X Log2 = Log8

@Stylux-z1p 2 часа назад

^ --> means raise to the power of 2^x = 9 --> when searching for the exponent, logarithms are involved Rewrite 2^x = 9 to logarithmic form log₂(9) = x log₂(9) = x 2log₂(3) = x ------------------------------------------------------- log₂(9) = x log₂(3 * 3) = log₂(3) + log₂(3) = x ------------------------------------------------------- log₂(9) = x (log(9)) / (log(2)) = 3 ---> the base-2 log change to natural log

@marccracchiolo4935 17 часов назад

Great video it’s so easy to forget this stuff you make it easy to remember & understand

@panlomito 20 часов назад

I must admit I do know this one has to be solved with log but I don't have the routine to get the equation right. Acoustics wasn't my thing at school.

@tomtke7351 18 часов назад

HEY, Ya'All ... don't forget to click thumbs up!

@mauriziograndi1750 19 часов назад

Ln9 / ln2 = 3.169925 2^3.169925 = 9

@femaleKCRoyalsFan 20 часов назад

This must be advanced algebra because I never had anything like this in high school

@sinapisalba 13 часов назад

We did, in last year...

@raya.pawley3563 18 часов назад

Thank you!

@robertroemer4233 19 часов назад

In the last step teacher didn't explain how to enter the logs in their calculators to arrive at the answer

@dazartingstall6680 19 часов назад

It'll depend on the calculator. In the windows calculator it's: 9 [log button] ÷ 2 [log button] =

@louf7178 18 часов назад

This is literally what log_2(9) means. (logarithm base 2 of 9)

@sylvieaubry1324 19 часов назад

Many thanks Blessing to you always

@thomasharding1838 16 часов назад

3.1699 which rounds at the thousandth place to 3.170

@flashtheoriginal 13 часов назад

That was an education

@johnmarchington3146 14 часов назад

My answer is log9/log2 but I haven't done the calculation (although I remember that log 2 = 0.3010)

@ceeemm1901 15 часов назад

Ok now that we've solved the problem and got 3.169 as the exponent, how can I write that out longhand. That is,i f the exp. was 4, I could write that out as 2x2x2x2. But now the exp. is 3.169 so how does it show in the real world...2x2x2x?.......

@dazartingstall6680 12 часов назад

The far easiest method is to type 2^3.169 into a calculator. But if you're a really dedicated glutton for punishment... First convert it into a fraction: 3169/1000 Then raise 2 to that fraction: 2^(3169/1000) In practice, this means raising 2 to the 3169th power, then taking the 1000th root of the result.

@crodz530 15 часов назад

I remember doing this in first grade.

@sanm4836 17 часов назад

Take log of both sides.

@cyruschang1904 11 часов назад

2^x = 9 = 3^2 x = (2log3)/(log2)

@markmauldin1327 2 часа назад

2 * log(3) / log(2)

@marais75012 Час назад

14 minutes for a three second problem??

@elainemessier8066 19 часов назад

X=3.169

@tomtke7351 18 часов назад

you didn't show your work but full credit as you got right answer

@katheesterbenz6892 10 часов назад

1.5

@leetucker9938 18 часов назад

x=3.17

@terveratsar5423 Час назад

Annoying unnecessary talking and repetitive nonsense

@WescottDesrosiers-m6w 15 часов назад

9 divide 2 = 4.5 so the final result is X=4.5

@markhessling831 11 часов назад

If it was 2x=9, then x would be 4.5. Unfortunately, it’s a log question, so that is incorrect.

@pappyoh1 17 часов назад

@whenindoubt1000 5 часов назад

Did you know that x is the exponent?

@gracejaklik2617 19 часов назад

Too much chatting and advertising your channel

@tomtke7351 19 часов назад

you're free to go elsewhere... but as a parting thought, did you ever have an educator flood your brain with new schooling thst just overloaded and over whelmed you? His chatty approach allows material to soak in being surrounded with familiar but unimportant data. Learning, especially math, is repetition... So... bye... and good luck... clearly your mind needs intense challenges that John doesn't offer AND ISN'T CHANGING HIS APPROACH JUST FOR YOU!

@dazartingstall6680 19 часов назад

I don't understand why people leave comments like this. If the style isn't to your taste, just move on.